In this paper the purpose and manner of conducting the process of asymptotic homogenization of a type 1-3 composite structure are presented. The formulation of the homogenization process is reduced to numerical static analysis of an elementary symmetry cell of the composite with generalized forces applied at the boundaries of material phases. It is demonstrated that the effective values of the material tensors of the composite depend not only on the tensors of the component materials, but also on variability course of the aforementioned tensors defined over the volume of the solid of an elementary symmetry unit of the composite. The latter factor becomes particularly significant in the case of a step-like discontinuity which occurs, e.g., in the type 1-3 composite structure.